A fundamental type of disorder that arises in jammed athermal systems is polydispersity in particle sizes [1]}, [2]}, [3]}, [4]}, which leads to amorphous energy minimized structures. This variation in particle sizes give rise to sources of localized stress within the material and are usually referred to as stress defects [5]}, [6]}. Such defects play an important role in the bulk properties as well as the dynamics of amorphous systems.
At the continuum scale stress defects have been modeled using bulk properties such as the elastic moduli of the medium and defect  [7]}, [8]}, however theories that incorporate microscopic disorder in the material are still missing. When the finite sizes of particles are considered, constructing coarse grained elasticity theories that account for disorder at the granular level becomes hard [9]}.
At the local scale, the non-linearities involved in mechanical equilibrium conditions become important, as they have to be simultaneously satisfied by the entire configuration. This has made the characterization of athermal disorder and consequently the construction of statistical mechanical theories challenging [10]}, [11]}, [12]}, [13]}.
